Closed loop MEMS pendulous accelerometers typically use torque rebalance with a voltage-controlled capacitive actuator to hold the pendulum at null. Assuming the actuator is stable, the voltage applied is proportional to acceleration. The accelerometers are calibrated to obtain the scale factor (acceleration to voltage proportionality). In the present implementation, the torque applied is not measured directly. The voltage is but the actuator may change and therefore the actual applied torque is not known. The accuracy and stability of the accelerometer will be dependent on the accuracy and stability of the applied voltage and the actuator functional stability, thereby limiting scale factor accuracy if only the voltage is measured. To rectify this problem and thereby increase performance especially of the MEMS accelerometers, the stability in the components becomes more critical. In the GRA the instability in the components is largely overcome by measuring the applied torque rebalance by directly measuring the actuator functions.
In the Pendulous Integrating Gyro Accelerometer (PIGA), a single degree-of-freedom (SDF) gyro is mounted onto a rotating platform that allows the gyro to be rotated about its Input Axis. The gyro contains a wheel that spins about the SRA (Spin Reference Axis). The wheel is mounted to a gimbal that can rotate about the Output Axis (OA). The gimbal is mounted within a case that is in turn attached to the rotating platform via a post. The SRA and OA are orthogonal. During operation, in response to a rotation of the case about the gyro Input Axis, the gyro gimbal responds with a rotation about the Output Axis. By rotating the platform, the same gimbal rotation will result.
To make a PIGA, the gyro is made purposely unbalanced by the addition of a mass along the SRA axis, to convert the gimbal into a pendulum. Under acceleration, the unbalanced mass generates a torque that tends to rotate the gimbal about the OA. By rotation of the platform (servo member) in the appropriate direction, the gimbal can be returned to its null position. Note that the pendulous torque and the gyro torque act on a common member, the gimbal. For this reason the gimbal is referred to as a Torque Summing Member (TSM).
The PIGA equation of motion for the gimbal rotation angle θ is given byI{umlaut over (θ)}+D{dot over (θ)}+Kθ=Hspin{dot over (φ)}−Pa  (1)where Hspin{dot over (φ)} is the gyro torque; Pa is the pendulous torque; Hspin=Iwheel{dot over (α)}spin is the wheel angular momentum; Iwheel is the wheel moment of inertia about the spin axis;{dot over (φ)} is the rotation rate of the platform; {dot over (α)}spin is the spin rate of the wheel; P is the pendulosity; andα is the input acceleration. In closed loop operation, the gyro torque is equal to the pendulous torque, Hspin{dot over (φ)}=Pa. The acceleration is then given by
                    a        =                                            H              spin                        P                    ⁢                      ϕ            .                                              (        2        )            where
      H    spin    Pis the Scale Factor.
One unique attribute of the PIGA is that when both sides of equation (2) are integrated, the following expression is obtained
                    v        =                                            H              spin                        P                    ⁢          ϕ                                    (        3        )            This expression represents the mechanical integration of acceleration, and the velocity is given directly by the Servo Member angle. The significance of this is that numerical integration is not required and a source of random walk in velocity is eliminated.
A second PIGA attribute is that the accuracy of the measurement only depends on the measurement of the platform angle for the velocity read-out or the rate of the platform rotation for the acceleration read-out, since the wheel speed is maintained constant by a synchronous drive motor whose speed is determined by the drive frequency only, and not on the magnitude of the voltages/currents applied to spin the wheel and rotate the platform. This attribute is possible because a very stable gyroscope is used to provide a very accurate rebalance torque.
The Gyro-Rebalanced Accelerometer (GRA) is intended to overcome the instability of torque rebalance components by applying a gyroscopic torque that can be measured directly. The principle has been shown in U.S. Pat. Nos. 5,457,993, 5,691,470 and 5,712,426. The disclosures of each of these patents are incorporated herein by reference. The significance of this approach is that the acceleration-produced torque is balanced by a gyroscopic torque; both are inertial torques.